Solid descending flow due to gravity is frequently applied to industri
al processes. Several kinds of models have been proposed like the plug
flow model, the potential flow model, the kinematic model, etc. In th
is study, a viscous flow model based on the Navier-Stokes equation has
been developed and was compared with the potential flow and the kinem
atic models. Both two and three dimensional experimental apparatuses h
ave been constructed to observe the velocity fields. The concept of so
lid viscosity was quoted to describe the friction between particles an
d the value was obtained from the experimental data. Slip boundary con
dition was used at the wall and the friction between particles and the
wall or the dead zone was expressed by the Fanning equation. Navier-S
tokes equation was applied to simulate the solid flow. The good agreem
ent between the observed and computed results was obtained in differen
t scale apparatuses at different solid descending velocities. The comp
utation results gave about 0.07 Pa.s as the solid viscosity of sand pa
rticles with the diameter of 0.001-0.002m. The solid-gas countercurren
t flow was also simulated by the Navier-Stokes equation with the same
value of solid viscosity.